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# 5.20 = 1.125^x

### 2 Answers by Expert Tutors

Yin C. | Tutoring in the MountainsTutoring in the Mountains
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To solve this, you must work backwards and deal with logarithms.

5.20 = 1.126^x

log (5.20) = x log 1.125

x = (log 5.20)/(log 1.125)

x = 13.997...rounding to 14
Isa R. | Test Prep, Maths and Social SciencesTest Prep, Maths and Social Sciences
4.5 4.5 (20 lesson ratings) (20)
0
The First step to this problem is recognizing what you wish to find: that is the value of x. Then realize that every other part of the equation is a constant non x value.

The next is to recall what properties you can use to manipulate the equation.

Looking at this equation, with our variable as an exponent leads me to think of using the properties of logarithms:  lnx^y =ylnx

5.20 = 1.125^x

So the first thing I do is take the natural log of both sides:

ln5.2 =ln1.125^x

Does this form look familiar?

ln5.2= xln1.125

From this point it is a simple algebra equation and we solve for x

ln5.2/ln1.125=x

Solving from here gets you a numerical value of x≅13.9974200563